Use the graphical method to construct the shear$-$force and bending$-$moment diagrams for the beam shown. Let $a=8\mathrm{.}5ft,b=6\mathrm{.}5ft,$ Determine the shear force acting at each of the following locations:

$($a$)x=8\mathrm{.}5-$ ft $($i$.$e$.,$ just to the left of the support $B)$

$($b$)x=8\mathrm{.}5+ft($i$.$e$.,$ just to the right of the support $B)$

$($c$)x=15\mathrm{.}0ft($i$.$e$.,$ at point C$)$

$($d$)x=26\mathrm{.}0-$ ft $($i$.$e$.,$ just to the left of support $D)$

$($e$)x=26\mathrm{.}0+ft($i$.$e$.,$ just to the right of support $D)$

When entering your answers, use the shear$-$force sign convention detailed in Section $7\mathrm{.}2.$

Answers:

$($a$)V=$

$$

kips

$($b$)V=$

i

kips

$($c$),V=$

i

kips

$($d$)V=$

kips

$($e$)V=$

kips The shear$-$force diagram crosses the $V=0$ axis between point $C$ and support $D.$ Determine the location $x_{CD}($measured from $A)$

where $V=0$ kips.

Answer: $x_{CD}=$

$ft$

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Attempts: unlimited

Part $4$

Determine the bending moment acting at each of the following locations:

$($a$)x=8\mathrm{.}5ft($i$.$e$.,$ at support B$)$

$($b$)x=15\mathrm{.}0ft($i$.$e$.,$ at point C$)$

$($c$)x=26\mathrm{.}0ft($i$.$e$.,$ at support $D)$

$($d$)x=31\mathrm{.}0ft($i$.$e$.,$ at point $E)$

When entering your answers, use the bending$-$moment sign convention detailed in Section $7\mathrm{.}2.$

Answers:

$($a$)M=$

kip$-$ft

$($b$)M=$

kip$-$ft

$($c$)M=$

kip$-$ft

$($d$)M=$

kip$-$ft Determine the bending moment acting at $x=x_{CD}($calculated in Part $3)$ where $V=0$ kips between support $B$ and point $C.$

Answer: $M=$

kip$-$ft

$c=11\mathrm{.}0ft,d=5\mathrm{.}0ft,w_B=5\mathrm{.}5$kip$\frac{s}{f}t,$ and $w_{CE}=2\mathrm{.}5$kip$\frac{s}{f}t.$ Construct the shear$-$force and bending$-$moment diagrams on paper and

use the results to answer the questions in the subsequent parts of this $GO$ exercise.

Calculate the reaction forces $B_y$ and $D_y$ acting on the beam. Positive values for the reactions are indicated by the directions of the

red arrows shown on the free$-$body diagram below. $($Note: Since $B_x=0,$ it has been omitted from the free$-$body diagram.$)$

Answers:

$B_y=$

kips

$D_y=$

i

kips